Although fairly new in the PDA market, Linux is slowly becoming a prominent player in specialized mobile devices. As an alternative to the recently deceast Palm OS, and Microsoft's Windows Mobile, companies are picking up Linux because it's open source(a lot of possibilities), powerful, and inexpensive.
Many US PDA's do not natively support Linux. Usually Linux is installed next to the PDA's main OS through exploits or hacks. Japan, however, has begun to embrace Linux in their PDA products. Sharp's Zaurus line of PDA's exclusively uses Linux as its primary OS.